The Center for American Progress reports [thinkprogress.org]
After Senate Majority Leader Mitch McConnell's (R-KY) decision to prevent a president of the opposite party from nominating anyone to the Supreme Court, it's doubtful that any justice will ever be confirmed again when the presidency is controlled by a different party than the Senate. That means America will lurch back and forth between extended periods with a understaffed Supreme Court, followed by massive shifts in the law as one party fills a backlog of vacancies.
[...]Several states have shown that there is a better way [than what, it appears, will happen at the federal level from now on].
- The Missouri plan
As America struggled through the Great Depression, Missouri's courts were a den of partisanship and corruption [mo.gov]. As former Chief Justice of Missouri Michael Wolff explains, judges were "selected in elections in which nominees were chosen by political parties under a patronage system." In much of the state, judges were selected by a single machine party leader, "Boss" Tom Pendergast. Throughout Missouri, "judges were plagued by outside political influences, and dockets were congested due to the time the judges spent making political appearances and campaigning."
Frustrated with their politicized judiciary, the people of Missouri passed a ballot initiative replacing the state's corrupt process with a non-partisan coalition--at least for the state's top judges.
When a vacancy arises on the state's supreme court, a seven person commission [mo.gov] consisting of "three lawyers elected by the lawyers of The Missouri Bar . . . three citizens selected by the governor, and the chief justice" submits three candidates to fill that vacancy to the state's governor. The governor then has 60 days to choose among those three names. If the governor fails to meet this deadline, the commission selects one of the three.
Finally, after a year of service, the newly appointed judge must survive a retention election, where a majority of the electorate can cast them out of office--though this only happens rarely.
This method of judicial selection, as well as variants upon it, was adopted by many states since its inception in Missouri.